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In online social networks, it is common to use predictions of node categories to estimate measures of homophily and other relational properties. However, online social network data often lacks basic demographic information about the nodes. Researchers must rely on predicted node attributes to estimate measures of homophily, but little is known about the validity of these measures. We show that estimating homophily in a network can be viewed as a dyadic prediction problem, and that homophily estimates are unbiased when dyad-level residuals sum to zero in the network. Node-level prediction models, such as the use of names to classify ethnicity or gender, do not generally have this property and can introduce large biases into homophily estimates. Bias occurs due to error autocorrelation along dyads. Importantly, node-level classification performance is not a reliable indicator of estimation accuracy for homophily. We compare estimation strategies that make predictions at the node and dyad levels, evaluating performance in different settings. We propose a novel "ego-alter" modeling approach that outperforms standard node and dyad classification strategies. While this paper focuses on homophily, results generalize to other relational measures which aggregate predictions along the dyads in a network. We conclude with suggestions for research designs to study homophily in online networks. Code for this paper is available at https://github.com/georgeberry/autocorr.